How does sl2 work? We know that, by KLRW algebra, the planar version, modulo some stop, there is only one way to realize the categorification.

I bet, we can do a purely downstairs theory, even define it.

So, how do we define it? Suppose, we say that hom betewen T-branes follows KLRW algebra, then what?

all the homs are in degree zero?